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Unformatted text preview: Math 16A March 18, 2006 Final l.(5,5,5,5) Evaluate the following derivatives. DO NOT SIMPLIFY.
a) a(x) = 4x3 — 3x/J:
(b) b(x) = tan(2x3)
, sin(2x)
(c) em) =
cos(x)
\ d — x/ 3 2* (d) (X) — 6 . dy . 2 _
2.(10)F1nd d— if xy +3y+12=0 wheny=4 andx= -2. x 3.( 10) Find the equation of the line tangent to the curve y = 2sin(x) —— 3cos(2x) when x = 0.
4.( 16) Find all values of x such that the graph of y = f(x) = x4 + x3 is: strictly increasing; strictly decreasing; concave up; and concave down. i . . dy
5.( 10) Pat saw the equation xs1n(y) + ycos(x) = 2 and computed;— = 0.6 , when
x x = 2 and y = 1t/2. Assuming Pat's computation of the derivative is correct, estimate y when x = 1.97.
6.( 15) The old farmer up the road, Mr. McDonald, wants your help in designing two identical rectangular pens side by side with a single common side for the least
possible cost. Each pen should have an area of 600 square feet. Fencing on the
outside of the two pens cost $5 per foot and fencing between the pens costs $3 per
foot. To the nearest 0.01 foot, what should be the dimensions of each pen? Page 2 of 10 Math 16A(5) March 18, 2006 Final Dr. Sallee /—\
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w 7.(l 5) Find the value ofx which maximizes X26 if x+ y =10 where x 3 0 and y _>_ 0. 8.(2()) A rotating laser level rotates once every 2
seconds and shines a tiny red spot of light as
it turns. The laser (L) is placed 50 feet
directly west of point A on a long ﬂat wall.
Point B is 50 feet north of point A on the
wall. If you were measuring the speed of the
spot of light at point B, how fast (in feet/sec)
would it appear to be going? 9.(20) The graph of the equation x2 + 4xy + 6 y2 — 30 = 0 generates an ellipse. Find the
largest and smallest values of y that satisfy the equation. l().( l4)An fellow student brings you some data acquired by measuring the force in Gs
(l G = normal force of gravity at surface of the earth) backward on a piece of
equipment in a test of a new braking system as a function of time. He wants to
know how fast the force is changing at 3 seconds. Explain how you would tell
him to approach the problem and why you would do it that way. Sec .1 1.99 6.44107
2.99 0.02065
3.99 4.25864
2.01 —2.82158
3.01 -0.01637
4.01 4.3004 Page 3 of 10 ...
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